Re: Are you a "Mental Gymnast"?

[David Purdue <dp18367 -at- iplanet -dot- com>]

Your assumption that the two events (1st choice of door and
2nd choice of door) are independant is a fallacy.  While there
is no causative link between the events, you have more information
to hand when you make the second choice than when you make the
first.  You also assume that the second choice is random rather
than directed (if you made the 2nd choice at random, then I
agree the chance would be 50-50, but Monty lets you make a
decision based on info to hand, so you can do better).

What you are forgetting is that Monty knows something that you
don't (he knows where the prize is).  When he opens the door
that has the joint property of not being one you picked and not
having the prize HE HAS GIVEN SOME OF THE INFORMATION HE HAS!

Let's take it step by step.

You pick a door.  There is now a 2/3 chance that the prize is
behind a door you did not pick.

Monty open a door, and shows that there is no prize there.

Now here is the tricky bit - Monty opening the door does not
change the chance of you picking right the first time.  In other
words - there is still a 2/3 chance that you picked wrong the
first time, so there is STILL, even with the door open, a 2/3
chance that the prize is behind one of the doors you did not
pick - even though you can now SEE behind one of those doors.

This is imprtant - so repeat after me:  There is a 2/3 chance
that I picked wrong the first time and nothing in the future
will chance the fact that in the past there was a 2/3 chance that
I picked wrong.

So what Monty is really giving you the chance to do is choose
one of the doors you did not pick before.  But you have additional
information, you know one door that the prize is definitely not
behind, and you know that there is a 2/3 chance that the prize
is behind one of the two doors you did not pick, so your best bet
(driven by logic, not emotion) is to pick the door that you did
not pick before and that Monty has not opened.  This gives you
a 2/3 chance of getting the prize.


=-=-=-=-=
Kevin McLauchlan wrote:

Thoughts?

Yes. My thought is that their answer (FAQ item 2.4)  is horse-pucky.

The fallacy is that their answer assumes some sort of causative 
connection between the two choices.

Your first choice was random, 1 of 3. Other than superstition, you had 
no reason to choose any one door over the others.  And it doesn't matter 
to the outcome, because you don't get your answer from that choice. The 
fact that you are even asked to make a choice at that point is just a 
red herring.


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